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Curve Fitting of Test Data
One of the main features of RocData is the ability to input strength test data from triaxial or direct shear tests, in order to determine the "best fit" strength envelope and the associated strength parameters (e.g. cohesion and friction angle) for a rock or soil material. The data can be obtained from lab tests of intact samples, or field data from in-situ rock mass tests.
Best-fit strength envelope for triaxial test data
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Triaxial test data is defined by major and minor principal stress at failure
(sigma1/sigma3 data pairs).
Direct shear test data is defined by normal and shear stress at failure
(sigN/tau data pairs).
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The following table summarizes the type of test data which can be analyzed for each strength criterion.
Summary of strength criteria and stress data types analyzed
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Curve Fitting: Triaxial Lab Data
Triaxial strength data from lab tests of rock or soil samples can be curve-fitted to the Generalized Hoek-Brown, Mohr-Coulomb or Power Curve strength models. The data is entered with the Use Lab Data dialog, shown below. The data can be entered into the spreadsheet in the dialog or imported from a file.
Use Lab Data dialog, Hoek-Brown criterion
The following table summarizes the input and output parameters for curve-fitting of triaxial strength data from lab tests, for each strength criterion.
Summary of input and output parameters for triaxial lab data analysis
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Curve Fitting: Triaxial Field Data
Triaxial strength data from field tests (e.g. strength tests on in-situ rock masses, or observed rock mass failures under known stress conditions) can be analyzed with the Use Rock Mass Data option. This allows you to perform a curve fit of triaxial data in order to determine the best fit strength envelope using the Generalized Hoek-Brown strength criterion.
Summary of input and output parameters for triaxial field data analysis
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Curve Fitting: Direct Shear Data
Direct shear strength data from lab tests of rock or soil samples can be curve-fitted to the Mohr-Coulomb, Barton-Bandis or Power Curve strength models. The data is entered with the Use Lab Data dialog, shown below. The data can be entered into the spreadsheet in the dialog or imported from a file.
Use Lab Data dialog, direct shear data, Barton-Bandis criterion
Summary of input and output parameters for direct shear data analysis
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Curve Fitting Method
RocData provides three curve-fitting methods for fitting strength envelopes to test data:
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Levenberg-Marquardt
Simplex
Linear Regression
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The curve fitting method is selected in the data entry dialog. New parameters are calculated as soon as a curve-fitting method is chosen. The following table summarizes the curve-fitting methods available for the different strength models.
The Levenberg-Marquardt method is the default technique for fitting strength criteria to data points. This robust algorithm has become the standard for non-linear regression. It is very reliable in practice, and has the ability to converge quickly from a wider range of initial guesses than other typical methods. Simplex and Linear Regression methods are also available.
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Curve Fitting: Residuals
After a curve-fitting has been performed, RocData reports a Residuals value. The Residuals is a measure of how well a strength criterion fits a data set. It is equal to the sum of the square of the vertical distances of the given data points from the fitted curve. The goal of the curve fitting computation is to determine the strength envelope which minimizes the value of the Residuals.
Residuals value displayed in dialog
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Curve Fitting: Display of Test Data
When triaxial data is displayed on the failure envelope plots, the data is plotted as points on the principal stress plot (sigma1 versus sigma3), and as Mohr Circles on the shear-normal plot. This is illustrated in the following figure.
Display of triaxial test data on failure envelope plots
For direct shear data, the data is plotted as points on the shear-normal plot. Direct shear data does not appear on the principal stress plot.
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